You'll probably end up with a new starter and/or thicker battery cables. I think your starter is getting weak, to be honest. You should take it to a parts store and have them test it, paying particular attention to the amperage draw. Good luck.
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Capri306, Moderator, The Mustang Works Online
1979 Mercury Capri, 5.0L -- C4 -- 2.73
1987 Mustang LX Notch